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Brownian motors belong to the class of nanoscale devices that use the thermal noise of the environment as one of the necessary components in the mechanism of their operation. Today, there are a lot of practical implementations of such nanomachines, both inorganic, fairly simple mechanisms produced artificially, and more complex ones created from separate biological components available at the cellular level. One of the options for implementing the mechanism of straightening the chaotic thermal noise of the environment into unidirectional motion is the presence of a motor particle in the field of action of an asymmetric periodic stationary potential, which undergoes certain small disturbances (fluctuations) periodically over time. To describe such asymmetric one-dimensional structures (for example, dipole chains or fibers of the cytoskeleton) in the theory of Brownian motors, two model potentials are most often used: piecewise linear sawtooth and double sinusoidal. In this work, within the framework of the approximation of small fluctuations, a model of a pulsating Brownian motor with a stationary double sinusoidal potential and a disturbing small harmonic signal is considered. A new method of parametrization of such a problem is proposed, which allows to separate the contributions from various factors affecting the operation of the ratchet, and the numerical procedure for calculating the average speed of the directional movement of nanoparticles for the selected type of model potentials is specified. A number of numerical dependences of the average speed on the main parameters of the system were obtained. Peculiarities of the behavior of the motor as dependent on the parameter responsible for asymmetry and the number of potential wells on the spatial period of the stationary potential have been investigated. It is shown that the direction of the generated flux of nanoparticles depends not only on the phase shift between the stationary and fluctuating components of the potential, but also on the temperature of the system and the frequency of fluctuations, i.e., a possibility of temperature-frequency control of the direction of movement in the considered model has been found. Diagrams have been constructed that allow you to choose the ratio between the parameters of the nanomotor to create a flux of particles in the desired direction. [ABSTRACT FROM AUTHOR]

It is well known that at low temperatures, the direction of motion for a quantum rocking ratchet in an asymmetric periodic potential (with a period L and an energy barrier V0), driven by an external fluctuating force F (F=0), can be opposite to the direction for the analogous classical ratchet operating at high temperature (Reimann et al, Phys. Rev. Lett. 1997, 79, 10). In the present work, within the semiclassical approximation and taking into account zero‐point fluctuations of a quantum particle in the minima of a sawtooth potential of an arbitrary asymmetry at the temperature of absolute zero, we obtain analytical expressions for the tunneling current in the rocking ratchet. These expressions allowed us to obtain the dependencies of the ratio FL/V0, at which the motion direction is reversed, on the asymmetry parameter and other parameters of the system. Similar results are obtained for a particle in a two‐sinusoidal potential. [ABSTRACT FROM AUTHOR]

We present a review of analytical approaches involved in developing the ratchet theory, which are based on the model of extremely asymmetric sawtooth potential. Analytical expressions are given for the average velocity of ratchets which operate in various motion modes, namely, motion induced by dichotomous half‐period shifts of potential profiles, adiabatic and high‐temperature modes, and motion induced by small fluctuations of an arbitrary type. The presence of jumps in the periodic extremely asymmetric sawtooth potential profile leads to a number of features of the obtained solutions which follow from the competition of the reverse sliding time tending to infinity with high fluctuation frequencies. The resulting dependences of the average velocity on the ratchet parameters clearly demonstrate that the motion direction can be controlled by tuning the frequency and temperature. The heuristic value of the presented models for controlling nanoparticle transport is discussed. [ABSTRACT FROM AUTHOR]

The operating properties of different‐type Brownian photomotors have been compared in relation to the symmetry interplay between their moving (particle/molecule) and immovable (substrate) units. As found, essentially different symmetry constraints and hence different motor behavior are characteristic of molecules if their electron density redistribution on excitation involves only odd‐order or only even‐order multipole moments. The two respective types of molecules give rise to dipole and quadrupole photomotors. Purely dipole photomotors can operate only on substrates with symmetric charge distribution and their ensemble with random molecular orientations undergoes equidirectional diffusion rather than directed motion. Contrary to this, purely quadrupole photomotors need substrates with antisymmetric charge distribution for directed motion to occur and they can move directionally in an ensemble. Also, quadrupole photomotors provide much smaller velocities of directed motion than their dipole counterparts (as a result of the much weaker interaction of quadrupoles than dipoles with an electric field). The generic distinctions between the two photomotor types are exemplified by donor‐acceptor‐substituted stilbenoids (dipole molecules) and symmetric squaraines (quadrupole molecules). The model used affords the rational design of photomotors by the selection of promising moving molecules and by the continuous wide‐range tuning of charge‐distribution symmetry in substrates. [ABSTRACT FROM AUTHOR]

Molecular devices that have an anisotropic periodic potential landscape can be operated as Brownian motors. When the potential landscape is cyclically switched with an external force, such devices can harness random Brownian fluctuations to generate a directed motion. Recently, directed Brownian motor-like rotatory movement was demonstrated with an electrically switched DNA origami rotor with designed ratchet-like obstacles. Here, we demonstrate that the intrinsic anisotropy of DNA origami rotors is also sufficient to result in motor movement. We show that for low amplitudes of an external switching field, such devices operate as Brownian motors, while at higher amplitudes, they behave deterministically as overdamped electrical motors. We characterize the amplitude and frequency dependence of the movements, showing that after an initial steep rise, the angular speed peaks and drops for excessive driving amplitudes and frequencies. The rotor movement can be well described by a simple stochastic model of the system.

Applicability of the effective one-dimensional equations, such as Fick-Jacobs equation and its extensions, describing diffusion of particles in 2D or 3D channels with varying cross section A(x) along the longitudinal coordinate x, is studied. The leading nonstationary correction to Zwanzig-Reguera-Rubí equation [R. Zwanzig, J. Phys. Chem. 96, 3926 (1992); D. Reguera and J. M. Rubí, Phys. Rev. E 64, 061106 (2001)] is derived and tested on the exactly solvable model, diffusion in a 2D linear cone. The effects of such correction are demonstrated and discussed on elementary nonstationary processes, a time dependent perturbation of the stationary flow and calculation of the mean first passage time. [ABSTRACT FROM AUTHOR]

Brownian motors are a class of nanomechanisms that generate directional motion of Brownian particles under nonequilibrium perturbations. A symmetry analysis of the factors affecting the appearance of a directed current and determining its direction indicates the dependence of the motor characteristics on the phase shift between the potential reliefs of the stationary and fluctuating components of nanoparticle potential energy. The motion of a Brownian particle located in the field of action of an extremely asymmetric stationary sawtooth potential fluctuating as a result of dichotomous effects of spatially harmonic signal is considered. Since the sawtooth potential is easily realized near a surface with a series of electrodes of a certain shape buried inside it, and the dichotomous changes of a spatially harmonic signal are easily created by laser beams, the considered motion of a nanoparticle (Brownian motor) can be realized experimentally. It is known that at sufficiently high temperatures, when the thermal energy exceeds the energy barrier of the sawtooth potential, the direction of motion is determined exclusively by the phase shift of the harmonic signal relative to the extrema of the sawtooth potential. In this article, an analytical expression for the motor average velocity has been obtained, which is valid at arbitrary temperatures, but at low frequencies of dichotomous fluctuations (adiabatic mode). An analysis of the expression has shown that there exists a critical temperature Tc below which the direction of motion loses its dependence on the magnitude of the phase shift, whereas at T > Tc the direction of motion is determined by that shift. In the region of intermediate temperatures T, for each value of the phase shift, one can indicate a temperature Ts > Tc such that at T < Ts the particle moves in one direction, while at T > Ts in the other. [ABSTRACT FROM AUTHOR]

A relevant and important question in studying the transport of nanoparticles is the possibility and methods of controlling the generated currents. One of the possibilities is to use the ratchet effect, i.e. the occurrence of directed motion as a result of the influence of nonequilibrium fluctuations of various nature when one or more symmetries in the system are broken. To implement the ratchet effect, a deterministic dichotomous process is often used, which can be modeled by two alternating states that have constant characteristics. Usually, the main factor determining the direction of motion of a Brownian motor is the spatial asymmetry of the potential profile. In certain cases, for example, for a double-well potential profile, one can relatively easily investigate the conditions for reversal of the direction of motor motion. In this paper, using the idea of Parrondo’s paradox games consisting of alternating strategies of a game that provides an average winning, we simulated the ratchet effect for a diffusion hopping model of an adiabatic Brownian motor with an asymmetric double-well on-off potential. The conditions affecting the direction of nanoparticle motion are investigated, the possibility of temperature control of the motion direction is shown, and an estimate of the generated average velocity of the Brownian motor in the adiabatic approximation is obtained. The motor functioning is simulated in terms of the game theory and the average trajectories of capital accumulation are obtained, which correspond to the trajectories of the average displacement of a Brownian particle due to the ratchet effect. For the chosen model, it is shown that, at low temperatures, a particle moves to the right in accordance with the simplest on-off ratchet model, while, at high temperatures, the motion reverses. A comparison of the simulation results with the values of the ratchet velocity obtained within the adiabatic approximation shows that this approximation becomes valid at sufficiently large values of the lifetimes of the states of the dichotomous process, and it turns out to be much more accurate in the high-temperature region than in the low-temperature one. [ABSTRACT FROM AUTHOR]

In spite of the widespread opinion about the negative effect of chaos on the nature and human life, there exist examples of its constructive role in various processes. Among them, a prominent position is occupied by the processes in which thermal noise causes not only Brownian motion but also drift of nanoparticles as a result of unbiased non-equilibrium perturbations of various nature in systems with broken spatial and/or temporal symmetry. Such processes are relevant to the operation of Brownian motors, or ratchets, actively studied in the past decades. In the present paper, the working principles of systems of this kind are explained based on the author’s approach which unifies the treatment of different ratchet effect manifestations in the models of fluctuating potential, catalytic wheel, and electroconformational coupling. Another manifestation of this effect is provided by the paradoxical games proposed by Parrondo in which chaos appears in random tosses of a die and the ratchet effect arises from a certain alternation of game strategies ensuring an average win. The paper presents the simplest version of Parrondo’s game; it consists in the alternation of two antisymmetric games, with the rules depending on the parity of the capital possessed by the player before the next toss. The dependence of the average win on the number of tosses is calculated by computer simulation and compared with the result of the catalytic wheel model valid in the adiabatic approximation. The theoretical win calculated by this model agrees well with the numerical simulation result for the game concerned. The attractiveness of the treatment of the ratchet effect in terms of game theory stems from the possibility to visualize the theoretical framework and to study the laws of Brownian motor operation by simple modelling methods. [ABSTRACT FROM AUTHOR]

The generalized Fick-Jacobs equation is widely used to study diffusion of Brownian particles in three-dimensional tubes and quasi-two-dimensional channels of varying constraint geometry. We show how this equation can be applied to study the slowdown of unconstrained diffusion in the presence of obstacles. Specifically, we study diffusion of a point Brownian particle in the presence of identical cylindrical obstacles arranged in a square lattice. The focus is on the effective diffusion coefficient of the particle in the plane perpendicular to the cylinder axes, as a function of the cylinder radii. As radii vary from zero to one half of the lattice period, the effective diffusion coefficient decreases from its value in the obstacle free space to zero. Using different versions of the generalized Fick-Jacobs equation, we derive simple approximate formulas, which give the effective diffusion coefficient as a function of the cylinder radii, and compare their predictions with the values of the effective diffusion coefficient obtained from Brownian dynamics simulations. We find that both Reguera-Rubi and Kalinay-Percus versions of the generalized Fick-Jacobs equation lead to quite accurate predictions of the effective diffusion coefficient (with maximum relative errors below 4% and 7%, respectively) over the entire range of the cylinder radii from zero to one half of the lattice period. [ABSTRACT FROM AUTHOR]

It is known that widths of spectral lines provide а researcher with a variety of important information: about properties of materials, nature of particles interaction, physical parameters of an environment, etc. By analogy with a study of spectral lines, this article analyzes behavior of the width of a bell-shaped frequency dependence of the average velocity of Brownian particles described by a model of a stochastic Brownian motor with asymmetric dichotomous fluctuations of particle potential energy. The bell-shaped dependence is explained by the disappearance of the motor effect in both the low- and high-frequency limits. The relations for the average particle velocity in the adiabatic (low-frequency) and high-temperature regimes of motion allowed us to analyze the frequency dependences for different values of the temporal asymmetry parameter ε of the fluctuations and the ratio α of potential energy amplitudes in two states of the dichotomous process. The invariance of characteristics of an adiabatic Brownian motor with respect to the asymmetry parameter allowed us to assume the effect of one-sided broadening of the frequency dependence of the velocity with changing ε and α. To confirm this assumption, the high-temperature behavior of a Brownian motor with a biharmonic potential energy (described by a sum of two sinusoids) is considered. Graphic dependences of the average velocity on the fluctuation frequency are obtained, which coincide in the adiabatic regime of motor functioning. Using the numerical procedure, frequencies of maxima and widths of the distributions have been calculated dependent on the temporal asymmetry parameter of fluctuations ε and the ratio α. The calculated dependences confirmed the assumption about the one-sided broadening of the bell-shaped frequency dependence of the average velocity of a Brownian motor. [ABSTRACT FROM AUTHOR]

Highlights • Determination of dominating relaxation mechanisms from temperature-dependent spectra. • Comparison of Fokker–Planck simulations with experimental MPS data. • Sharp bends in harmonic spectra attributed to superimposing and coupled relaxation. Abstract Magnetic Particle Spectroscopy (MPS) is a characterization method for investigating the nonlinear properties of magnetic nanoparticles (MNP) using magnetic field strengths in the order of a few tens of millitesla. Its exploitation for particle characterization is of high significance for biomedical applications such as Magnetic Particle Imaging (MPI) and magnetic hyperthermia. Since the dynamic characteristics of MNP are influenced by both the Néel and the Brownian relaxation mechanism, harmonic spectra in MPS measurements are directly linked to ambient influences like temperature or viscosity of the surrounding medium. Experimental data of multiparametric measurements helps one to evaluate and validate mathematical models of dynamic particle magnetization. This contribution deals with the investigation of temperature-dependent harmonic spectra of different commercially available single-core and multi-core particle systems. It is shown, that dominating relaxation mechanisms can be determined from temperature-dependent MPS measurements. [ABSTRACT FROM AUTHOR]

Graphical abstract Abstract Multiple experiments show that various submicron particles such as magnetosomes, RNA messengers, viruses, and even much smaller nanoparticles such as globular proteins diffuse anomalously slow in viscoelastic cytosol of living cells. Hence, their sufficiently fast directional transport by molecular motors such as kinesins is crucial for the cell operation. It has been shown recently that the traditional flashing Brownian ratchet models of molecular motors are capable to describe both normal and anomalous transport of such subdiffusing cargos by molecular motors with a very high efficiency. This work elucidates further an important role of mechanochemical coupling in such an anomalous transport. It shows a natural emergence of a perfect subdiffusive ratchet regime due to allosteric effects, where the random rotations of a "catalytic wheel" at the heart of the motor operation become perfectly synchronized with the random stepping of a heavily loaded motor, so that only one ATP molecule is consumed on average at each motor step along microtubule. However, the number of rotations made by the catalytic engine and the traveling distance both scale sublinearly in time. Nevertheless, this anomalous transport can be very fast in absolute terms. [ABSTRACT FROM AUTHOR]

Abstract Under the background of subdiffusion in cytosol, the nonlinear-coupling fractional Langevin equations is proposed to model the stepping modes of the double-headed molecular motor: inchworm and hand-over-hand mechanisms, and the transport properties in flashing asymmetrical periodic potential are investigated. By numerical simulations, the influences of noise intensity, height of potential barriers, and external load force on the average velocity of coupled particles current in the overdamped limit are assessed. With the exception of conventional directed transport, we observe some anomalous phenomena, including inverse transport and cooperative transport, which cannot be described by the integral-order models. Moreover, the average transport velocity varies non-monotonously with the noise intensity and the height of potential barrier, which shows there exists generalized stochastic resonance (GSR) phenomenon in proposed coupled fractional systems. The results also indicate that the damping force involving the weighted sum of historical velocity leads to the nonlocal memory property and blocks the traditional dissipative behaviors, and it even plays a cooperative role of the driving force in drift motion. Highlights • The model of fractional nonlinear-coupling Brownian motors are established. • Nonlinear coupling is considered to mimics the stepping modes in cytosol. • Subdiffusive transport behaviors of double-headed molecular motor are analyzed. • Inverse transport and generalized stochastic resonance are observed by simulations. • The directed transport and energy conversion can be controlled by the system parameters. [ABSTRACT FROM AUTHOR]

We consider the autonomous piston engine in a coupled cavity scheme in an optomechanical setup. Treating the radiation field as working fluid, we investigate the transduction of virtual photons due to ground state excitations. Rabi-like energy splittings and Casimir effect are shown by avoided crossing in the eigenfunction spectrum. Second order coherence functions are employed to analyze the bunching of the cavity and mechanical mode in optomechanical implementation of Brownian motors. The imbalance in occupation numbers of the working modes is investigated for the power for work extraction. We explore the guidance of the radiation field in work extraction. We study the synchronicity between virtual photon conversion and power in the mechanical mode. Generation and amplification of virtual photon transduction are modulated by mutual interactions between the qubit, piston, and mechanical mode in the absence of external driving fields. [ABSTRACT FROM AUTHOR]

Abstract The dynamics of autonomous Brownian motors that achieve rectified motion due to morphological changes is analyzed. These motors are assumed to be deformable, with restitution internal forces, and to be able to adapt their shapes as function of their total elongation. A generic protocol for morphology adaptation is presented which guarantees unidirectional motion at a constant average speed. This protocol is illustrated by diverse particular examples. Motors operating under non-linear internal forces are analyzed. It is shown that non-linear forces produce considerable variations of the average speed and could serve as a control mechanism for the biased dynamics. The effects of hydrodynamic interactions are quantified as function of the morphological asymmetry. Such interactions are found to promote a very slight reduction of the rectification phenomenon, and could be observable only for motors operating at extremely reduced velocities. The theoretical analysis is found to be in very good agreement with the results of Brownian Dynamics simulations. Highlights • Rectified speed of BMs under diverse morphologic changes is rigorously calculated. • It is shown that nonlinear restitution forces could control the rectified speed. • It is shown that hydrodynamic interactions do not affect the rectification mechanism. • Numerical simulations are used to support these predictions. • The model can be used as a tool for designing novel autonomous BMs. [ABSTRACT FROM AUTHOR]

The transport of an underdamped particle driven by an external force in a periodic asymmetric potential with color noises is investigated. The corresponding mathematical model is established. By the method of the numerical simulation, we present the movement of the steady current of underdamped particles. Different parameters have different influences on current transport, such as increasing or decreasing. It is shown that the cooperations among the external force and the noises parameter lead to the phenomena: when the external force is not zero, the large external force may cause the large current value or the absolute value of the current. The current value is due to the effect of the cooperations of external force and noise parameter. [ABSTRACT FROM AUTHOR]

In some complex viscoelastic mediums, it is ubiquitous that absorbing and desorbing surrounding Brownian particles randomly occur in coupled systems. The conventional method is to model a variable-mass system driven by both multiplicative and additive noises. In this paper, an improved mathematical model is created based on generalized Langevin equations (GLE) to characterize the random interaction with locally fluctuating number of coupled particles in the elastically coupled factional Brownian motors (FBM). By the numerical simulations, the effect of fluctuating interactions on collective transport behaviors is investigated, and some abnormal phenomena, such as cooperative behaviors, stochastic resonance (SR) and anomalous transport, are observed in the regime of sub-diffusion. [ABSTRACT FROM AUTHOR]

We study the temporal correlations in the evolution of the order parameter ϕ t for the Vicsek model with vectorial noise by estimating its Hurst exponent H with detrended fluctuation analysis (DFA). We present results on this parameter as a function of noise amplitude η introduced in simulations. We also compare with well known order–disorder phase transition for that same noise range. We find that – regardless of detrending degree – H spikes at the known coexistence noise for phase transition, and that this is due to nonstationarities introduced by the transit of the system between two well defined states with lower exponents. We statistically support this claim by successfully synthesizing equivalent cases derived from a transformed fractional Brownian motion (TfBm). [ABSTRACT FROM AUTHOR]

In this paper we have presented the dynamics of a Brownian particle which is coupled to a thermal bath in the presence of a fluctuating magnetic field (FMF). By virtue of the FMF the Brownian particle experiences a time dependent damping strength for the x − direction motion even in the presence of a stationary Markovian thermal bath. There is a transition state along this direction. The time dependent damping strength leads to appear a bi-turnover phenomenon in the variation of the barrier crossing rate as a function of the thermal bath induced damping strength. It is a generic signature of the fluctuating magnetic field. [ABSTRACT FROM AUTHOR]

Using an exact expression for the average velocity of inertialess motion of pulsating ratchets, a simple proof is given for the recently discovered hidden space-time symmetry of Cubero-Renzoni (D. Cubero, F. Renzoni, 2016). The conditions are revealed for the absence of the ratchet effect in systems with potential energies described by products of periodic functions of coordinate and time possessing the symmetry of the main types. In particular, it is shown that the ratchet effect is absent for the time dependence of the universal symmetry type (which combines three standard symmetries), and this restriction is removed when inertia is taken into account, unless the coordinate dependence of the potential energy is related to symmetric or antisymmetric functions. [ABSTRACT FROM AUTHOR]

Control and transport of nanoscale objects in fluids is challenging because of the unfavorable scaling of most interaction mechanisms to small length scales. We designed energy landscapes for nanoparticles by accurately shaping the geometry of a nanofluidic slit and exploiting the electrostatic interaction between like-charged particles and walls. Directed transport was performed by combining asymmetric potentials with an oscillating electric field to achieve a rocking Brownian motor. Using gold spheres 60 nanometers in diameter, we investigated the physics of the motor with high spatiotemporal resolution, enabling a parameter-free comparison with theory. We fabricated a sorting device that separates 60- and 100-nanometer particles in opposing directions within seconds. Modeling suggests that the device separates particles with a radial difference of 1 nanometer [ABSTRACT FROM AUTHOR]

The operating voltage of a nanoelectromechanical (NEM) relay can be scaled down significantly using negative capacitance (NC), which is a unique property of ferroelectric materials. It has been observed that a ferroelectric capacitor can amplify the internal voltage of a device (higher than the externally applied voltage) by means of the NC effect. In this simulation work, depending on the structural parameters of a ferroelectric capacitor and an NEM relay, an NC + NEM relay (in which the gate electrode of the NEM relay is connected in series to the ferroelectric capacitor) was investigated. As a result, a sub-0.5-V operating voltage is theoretically estimated. [ABSTRACT FROM AUTHOR]

In the paper, we investigate the transport properties of coupled flashing ratchets in viscoelastic media. Using generalized Langevin equation, subvelocity V α , subdiffusive coefficient D α and generalized Peclet number P e α are calculated as functions of the temperature T and the flashing period τ with different subdiffusive exponents α . The results show that the transport of coupled flashing ratchets can be optimized in viscoelastic media. [ABSTRACT FROM AUTHOR]

We suggest a new approach to description of driven diffusive systems in which fluctuations of nano-particle potential energy, being a source of directed motion, are considered as small. The base of the approach is the method of the Green's functions, which allow writing analytical expressions for the sought-for average nano-particle velocity. These expressions are essentially simplified under the assumption of high temperatures. Within this hightemperature approximation, we consider a system (Brownian motor) with small harmonic oscillations of the particle potential energy of a saw-tooth shape. The obtained representation for the average motor velocity is the product of two functions. One of them depends on the fluctuation frequency and the other includes geometrical parameters of the system (that is of the steady and perturbing potential profiles). It is shown that the frequency dependence of the average velocity is a nonmonotonic function with the maximum position determining by the inverse characteristic diffusion time. In its turn, the average motor velocity as a function of the asymmetry parameter of the nonfluctuating component of the potential profile and the phase shift of the fluctuating one is sign-changing. This result means that there exists a possibility to govern the direction of the motor motion by the phase shift of harmonic oscillations relative to a fixed saw-tooth potential component. The intervals of both the phase shift and the asymmetry parameter values, in which the particle can move to the right or to the left, are diagrammed. The regularities obtained are of great importance to choose the values of parameters which provide effective regimes of Brownian motors operation. [ABSTRACT FROM AUTHOR]

We study diffusion properties of an inertial Brownian motor moving on a ratchet substrate, i.e., a periodic structure with broken reflection symmetry. The motor is driven by an unbiased timeperiodic symmetric force that takes the system out of thermal equilibrium. For selected parameter sets, the system is in a non-chaotic regime in which we can identify a non-monotonic dependence of the diffusion coefficient on temperature: for low temperature, it initially increases as the temperature grows, passes through its local maximum, next starts to diminish reaching its local minimum, and finally it monotonically increases in accordance with the Einstein linear relation. Particularly interesting is the temperature interval in which diffusion is suppressed by the thermal noise, and we explain this effect in terms of transition rates of a three-state stochastic model. [ABSTRACT FROM AUTHOR]

The directed transport in a one-dimensional overdamped, Brownian motor subjected to a travelling wave potential with variable shape and exposed to an external bias is studied numerically. We focus our attention on the class of Remoissenet–Peyrard parametrized on-site potentials with slight modification, whose shape can be varied as a function of a parameter s , recovering the sine–Gordon shape as the special case. We demonstrate that in the presence of the travelling wave potential the observed dynamical properties of the Brownian motor which crucially depends on the travelling wave speed, the intensity of the noise and the external load is significantly influenced also by the geometry of the system. In particular, we notice that systems with sharp wells and broad barriers favour the transport under the influence of an applied load. The efficiency of transport of Brownian motors in deformable systems remains equal to 1 (in the absence of an applied load) up to a critical value of the travelling wave speed greater than that of the pure sine–Gordon shape. [ABSTRACT FROM AUTHOR]

The aim of the present work is to develop a theory of high-temperature polar molecular rotors, the rotation of which is initiated by an external alternating electric field. Such rotors can be considered as Brownian motors in the sense that a unidirectional translatory motion of motor particles is similar to the unidirectional rotation of moving part of a rotor; that allows using, at calculations, the high-temperature theory of Brownian motors. The potential energy of a rotating particle, as a function of time and rotation angle, is represented in additive-multiplicative form. The approximation of the two first harmonics suffices to describe a smooth potential profile. Indeed, they are the minimum number of harmonics to simulate the asymmetry of the potential relief and to describe molecular rotors since the first harmonic is conditioned by the interaction of the rotor with the alternating field and the second one - by the potential of hindered rotation. With these conditions, the velocity of rotation of polar molecular rotors is calculated, and the analytical dependences of the velocity on the parameters of the model is analyzed for the two cases of time dependence of the applied alternating electric field, harmonic and stepped. It is shown that, at a stepped change of an alternating electric field, the values of the angular velocity are higher, for any frequency of the applied field, than those at a harmonic change, and a dichotomic mode of the electric field changing is generally more efficient one, resulting in the optimal mode of rotor operation. Moreover, there exists a qualitative difference, in the low-frequency asymptotics of the rotor velocity, between harmonic and stepwise external field: the average velocity of rotation is proportional to the square of the field modulation frequency in the former case, and it is the linear function of the frequency in the later case. [ABSTRACT FROM AUTHOR]

Abstract: A detailed analysis of the adiabatic-piston problem reveals, for a finely-tuned choice of the spatial dimensions of the system, peculiar dynamical features that challenge the statement that an isolated system necessarily reaches a time-independent equilibrium state. In particular, the piston behaves like a perpetuum mobile, i.e., it never comes to a stop but keeps wandering, undergoing sizeable oscillations around the position corresponding to maximum entropy; this has remarkable implications on the entropy changes of a mesoscopic isolated system and on the limits of validity of the second law of thermodynamics in the mesoscopic realm.

The nonequilibrium thermodynamics feature of a Brownian motor operating between two different heat baths is explored as a function of time t. Using the Gibbs entropy and Schnakenberg microscopic stochastic approach, we hnd exact closed form expressions for the free energy, the rate of entropy production, and the rate of entropy flow from the system to the outside. We show that when the system is out of equilibrium, it constantly produces entropy and at the same time extracts entropy out of the system. Its entropy production and extraction rates decrease in time and saturate to a constant value. In the long time limit, the rate of entropy production balances the rate of entropy extraction, and at equilibrium both entropy production and extraction rates become zero. Furthermore, via the present model, many thermodynamic theories can be checked. [ABSTRACT FROM AUTHOR]

In probability theory, there is a counter-intuitive result that it is possible to construct a winning strategy from two individually losing (or at most breaking-even) "games" by alternating between them. The work presented here demonstrates the application of this principle to supported lipid bilayers (SLBs) in order to create directed motion of charged lipid components in the membrane, which was achieved through the use of "Brownian ratchets" in patterned SLBs. Both a finite element analysis model and an experimental setup have been used to investigate the role of key parameters for the operation of these ratchets: (1) the asymmetry of the ratchet teeth and (2) the relation of the ratchet height to the period of the applied electric field. Importantly, we find that the efficiency of the ratchet for a given charged species is dependent on the diffusion coefficient. This opens the possibility for separation of membrane species according to their size or viscous drag coefficient within the membrane. [ABSTRACT FROM AUTHOR]

We discuss an autonomous motor based on a Brownian particle driven from thermal equilibrium by periodic in time variation of the internal potential through which the particle interacts with molecules of the surrounding thermal bath. We demonstrate for such a motor the absence of a linear response regime: the average driving force and drift velocity are shown to be quadratic in both the frequency and amplitude of the variation. The adiabatic approximation (of an infinitely slow variation) and the leading correction to it (linear in the variation's frequency) both lead to zero drift and are insufficient to describe the motor's operation. [ABSTRACT FROM AUTHOR]

Effect of external periodic regulations on a symmetric Brownian motor performing between two temperature sources was investigated. By means of numerical calculations, we found that: (i) The regulations can control magnitude and direction of the motor's current to a large degree. As one of the motor's compartments is regulated, the motor's current can be both inversed and maximized, dependent on amplitude and frequency of the periodic driving force. If two periodic driving forces with identical amplitudes and frequencies are employed to regulate respectively two compartments of the Brownian motor, the current's magnitude and direction will make periodic oscillations with phase difference between them. In addition, the external periodic regulation can also change direction of thermal rectifier of the system as a switch. (ii) Optimal regulating parameters of the external periodic forces can enhance pronouncedly conversion efficiency of energy of the Brownian motor. [ABSTRACT FROM AUTHOR]

The paper contains mathematical justification of basic facts concerning the Brownian motor theory. The homogenization theorems are proved for the Brownian motion in periodic tubes with a constant drift. The study is based on an application of the Bloch decomposition. The effective drift and effective diffusivity are expressed in terms of the principal eigenvalue of the Bloch spectral problem on the cell of periodicity as well as in terms of the harmonic coordinate and the density of the invariant measure. We apply the formulas for the effective parameters to study the motion in periodic tubes with nearly separated dead zones. [ABSTRACT FROM AUTHOR]

We study a noisy drive mechanism for efficiency enhancement of Brownian motors operating on the microscale domain. It was proven [J. Spiechowicz et al., J. Stat. Mech. (2013) P02044] that biased noise η(t) can induce normal and anomalous transport processes similar to those generated by a static force F acting on inertial Brownian particles in a reflection-symmetric periodic structure in the presence of symmetric unbiased time-periodic driving. Here, we show that within selected parameter regimes, noise η(t) of the mean value 〈η(t)〉=F can be significantly more effective than the deterministic force F: the motor can move much faster, its velocity fluctuations are much smaller, and the motor efficiency increases several times. These features hold true in both normal and absolute negative mobility regimes. We demonstrate this with detailed simulations by resource to generalized white Poissonian noise. Our theoretical results can be tested and corroborated experimentally by use of a setup that consists of a resistively and capacitively shunted Josephson junction. The suggested strategy to replace F by η(t) may provide a new operating principle in which micro- and nanomotors could be powered by biased noise. [ABSTRACT FROM AUTHOR]

The study of the proteinaceous engines locomotion' mechanism is a current topic of interest, because it allows to explain different cell functions and simultaneously provides engines replications at nanometer scale. This study involves the understanding of stochastic phenomena at microscale in periodic systems with any kind of asymmetry and that are outside of the thermal equilibrium. In this way one system being studied that is out of thermal equilibrium and at the same time, is immersed in a universe with dissipation and generation of white thermal noise, which generates a directed movement and as the transportation phenomenon does, so that the system symmetry or asymmetry conditions are modeled. Since the discovery of Brownian motion, there have been carried out some of the most arduous investigations of the physical processes, that can be interpreted under this phenomenon and under the thermodynamics laws. From the microscopic point of view, the random thermal motion dominates this world and makes thermal fluctuations give rise to Brownian motion and Brownian motors. [ABSTRACT FROM AUTHOR]

The use of an ultrasound (US) field for rapid and reversible control of the movement of bubblepropelled chemically powered PEDOT/Ni/Pt microengines is demonstrated. Such operation reflects the USinduced disruption of normal bubble evolution and ejection, essential for efficient propulsion of catalytic microtubular engines. It offers precise speed control, with sharp increases and decreases of the speed at low and high US powers, respectively. A wide range of speeds can thus be generated by tuning the US power. Extremely fast changes in the motor speed (<0.1 s) and reproducible "On/Off" activations are observed, indicating distinct advantages compared to motion control methods based on other external stimuli. Such effective control of the propulsion of chemically powered microengines, including remarkable "braking" ability, holds considerable promise for diverse applications. [ABSTRACT FROM AUTHOR]